MAP DEMO This demonstration is a tool for experimenting with common map projections and great circle paths. All of the map projections are drawn by the MAP_SET IDL User's Library Procedure. The forward and inverse map transformations are built into IDL. The projections are described in more detail below. Great circles may be drawn with selected inclinations and equatorial crossings. You can draw the great circle connecting two selected points or cities, showing both the route and distance. A small data base of approximately 50 cities is included. Controls: >>> DONE Exit this demo. >>> RESET The "Reset" button sets the center latitude, longitude, and rotation to zero, and then re-draws the selected projection. >>> HELP Display this text. >>> MAP PARAMETERS Displays the control panel to select a projection, its center and rotation. >>> Cities/Circles Displays the control panel to mark cities, measure distances, and to draw great circles. >>> CONTINENTAL OUTLINES Continental outlines are suppressed or activated with this pulldown menu. >>> ELEVATIONS Activates and deactivates the display of elevation data. World elevations are obtained from a 1 degree longitude by 0.5 degree latitude data file included with IDL. These elevations are warped to the current map projection and displayed. Note: warping the image to the map will require a significant amount of time. The MAP PARAMETERS control panel has the following items: >>> PROJECTION TYPE Pick a map projection by clicking on the projection's button. >>> CENTER LATITUDE and LONGITUDE, ROTATION Vary the latitude and longitude of the center of the projection with the sliders. The Rotation slider sets the rotation of the polar axis with respect to the vertical. Positive longitudes are east of the prime meridian, negative longitudes are west of the prime meridian. >>> INVERSE TRANSFORMATIONS Clicking on a point in the map displays the latitude and longitude of the point. This illustrates the inverse transform capability, which given a screen coordinate returns its latitude/longitude. >>> CITIES / GREAT CIRCLES CONTROL PANEL Selecting a city shows its location on the map. Its latitude and longitude are displayed underneath the sliders. If the current map projection does not include the city, ***** is displayed in the latitude/longitude box. Draw the great circle connecting two points by clicking on the "Connect two points" button, and then clicking on the two points or selecting their locations from the city menu. The distance is also shown. Draw great circles with the given inclination and equatorial crossing set in the Great Circle Parameters sliders, by clicking on the "Draw Great Circle" button. ********* PROJECTIONS ********** >>> STEREOGRAPHIC The stereographic projection is an azimuthal, true perspective projection with the globe being projected onto the UV plane from the point P on the globe diametrically opposite to the point of UV tangency. The whole globe except P is mapped onto the UV plane. There is, of course, great distortion for regions close to P, since P maps to infinity. Commonly used for polar projections (set Center latitude to + or - 90 degrees). All great or small circles are shown as circular arcs or straight lines. >>> ORTHOGRAPHIC The orthographic projection is an azimuthal perspective projection with point of perspective at infinity. As such, it maps one hemisphere of the globe into the UV plane. Distortions are greatest along the rim of the hemisphere where distances and land masses are compressed. Usage: Pictorial views of the Earth, resembling those seen from space. All great circles are shown as elliptical arcs or straight lines. >>> CONIC The conic projection in this mapping package is Lambert's conformal conic with two standard parallels. It is constructed by projecting the globe onto a cone passing through two parallels. There is additional scaling to achieve conformality. The pole under the cone's apex is transformed to a point and the other pole is mapped to infinity. The scale is correct along the two standard parallels. Parallels are projected onto circles and meridians onto equally spaced straight lines. For this projection only, the Center Latitude Slider controls the latitude of one standard parallel, and the Center Longitude Slider controls the latitude of the other standard parallel. Primary usage is for large-scale mapping of areas of largely east-west extent. >>> LAMBERT'S EQUAL AREA Lambert's cylindrical equal area projection adjusts projected distances in order to preserve area. Hence, it is not a true perspective projection. Like the stereographic projection, it maps to infinity the point P diametrically opposite the point of tangency. Note also that to preserve area, distances between points must become more contracted as the points become closer to P. Lambert's equal area projection has less overall scale variation than the other azimuthal projections in this package. Recommended for equal-area mapping of regions near the Equator. >>> GNOMONIC The Gnomonic projection is the perspective, azimuthal projection with point of perspective at the center of the globe. Hence, with the gnomonic projection, the interior of a hemispherical region of the globe is projected to the UV plane with the rim of the hemisphere going to infinity. Except at the center, there is great distortion of shape, area and scale. All great circles are shown as straight lines. Used by navigators and aviators for determining courses. Too much distortion for many uses. >>> AZIMUTHAL PROJECTIONS With azimuthal projections, the UV plane is tangent to the globe. The point of tangency is projected onto the center of the plane and its latitude and longitude are P0lat and P0lon respectively. Rot is the angle between North and the V-axis. Important characteristics of azimuthal maps include the fact that directions or azimuths are correct from the center of the projection to any other point and great circles through the center are projected to straight lines on the plane. The IDL mapping package includes the following azimuthal projections: Stereographic, Orthographic, Gnomonic, Lambert's Azimuthal Equal Area and the Azimuthal Equidistant projection. >>> AZIMUTHAL EQUIDISTANT The azimuthal equidistant projection is also not a true perspective projection, because it preserves correctly the distances between the tangent point and all other points on the globe. The point P opposite the tangent point is mapped to a circle on the UV plane and hence the whole globe is mapped to the plane. There is, of course, infinite distortion close to the outer rim of the map, which is the circular image of P. The polar aspect is used for polar regions. The oblique aspects is used for world maps, centered on important cities. >>> SATELLITE Not completly implemented. >>> CYLINDRICAL The cylindrical equidistant projection is one of the simplest projections to construct. If EQ is the equator, this projection simply lays out horizontal and vertical distances on the cylinder to coincide numerically with their measurements in latitudes and longitudes on the sphere. Hence, the equidistant cylindrical projection maps the entire globe to a rectangular region bounded by -180 <= u <= 180, and -90 <= v <= 90. If EQ is the equator, meridians and parallels will be equally spaced parallel lines. >>> MERCATOR Mercator's projection is partially developed by projecting the globe onto the cylinder from the center of the globe. This is a partial explanation of the projection because vertical distances are subjected to additional transformations to achieve conformality --- that is, local preservation of shapes. To properly use the projection, the user should be aware that the two points on the globe 90 degrees from EQ (e.g., the North and South poles in the case that EQ is the equator) are mapped to infinite distances. >>> MOLLWIEDE With the Mollweide projection, the central meridian is a straight line, the meridians 90 degrees from the central meridian are circular arcs and all other meridians are elliptical arcs. The Mollweide projection maps the entire globe onto an ellipse in the UV plane. The circular arcs encompass a hemisphere and the rest of the globe is contained in the lunes on either side. >>> SINUSOIDAL With the sinusoidal projection, the central meridian is a straight line and all other meridians are equally spaced sinusoidal curves. The scaling is true along the central meridian as well as along all parallels. With this projection only, the Center Latitude and Rotation Sliders have no effect.